suppose a company receives 60% of its order the internet. what is the probability that the fifth order received is the first internet order?
what is the probability that the eight order received is the fifth internet order?
To calculate the probability that the fifth order received is the first internet order, we need to consider the cumulative probability of all previous orders not being internet orders, multiplied by the probability of the fifth order being an internet order.
Let's break down the problem into steps:
Step 1: Calculate the probability that each individual order is not an internet order.
Since the company receives 60% of its orders via the internet, the probability that each individual order is not an internet order is 40% or 0.4.
Step 2: Calculate the probability of the fourth order not being an internet order.
The probability that the fourth order is not an internet order is also 0.4.
Step 3: Calculate the probability of the fifth order being an internet order.
Since the company receives 60% of its orders via the internet, the probability that the fifth order is an internet order is 0.6.
Step 4: Calculate the cumulative probability.
The cumulative probability of the fourth order not being an internet order is multiplied by the probability that the fifth order is an internet order:
P(Fifth order is the first internet order) = P(Fourth order is not an internet order) * P(Fifth order is an internet order)
= 0.4 * 0.6
= 0.24 or 24%
Therefore, the probability that the fifth order received is the first internet order is 24%.
Now let's calculate the probability that the eighth order received is the fifth internet order.
Step 1: Calculate the probability that each individual order is not an internet order.
Since the company receives 60% of its orders via the internet, the probability that each individual order is not an internet order is 40% or 0.4.
Step 2: Calculate the probability of the fourth order being the first internet order.
To calculate this, we use a similar approach as in the previous question. The cumulative probability of the fourth order being the first internet order is multiplied by the probability that the fifth order is not an internet order:
P(Fourth order is the first internet order) = P(Third order is not an internet order) * P(Fourth order is an internet order)
= 0.4 * 0.6
= 0.24 or 24%
Step 3: Calculate the probability of the fifth order not being an internet order.
The probability that the fifth order is not an internet order is 0.4.
Step 4: Calculate the probability of the eighth order being the fifth internet order.
The cumulative probability of the fourth order being the first internet order is multiplied by the probability that the fifth order is not an internet order, and then the cumulative probability is further multiplied by the probability that the eighth order is an internet order:
P(Eighth order is the fifth internet order) = P(Fourth order is the first internet order) * P(Fifth order is not an internet order) * P(Eighth order is an internet order)
= 0.24 * 0.4 * 0.6
= 0.0576 or 5.76%
Therefore, the probability that the eighth order received is the fifth internet order is 5.76%.